Evaluation of Ordered Sequential Assimilation for Improved EnKF Sampling
K. Fossum and T. Mannseth
Event name: ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery
Session: Ensemble Methods
Publication date: 08 September 2014
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Ensemble based data assimilation (DA) methods, such as the (sequential) ensemble Kalman filter (EnKF) and the (non-sequential) ensemble smoother (ES), can both be utilized for solving the inverse problem of estimating poorly known parameters from data consisting of noisy observations of some dynamical system. For cases where we have non-linear data, i.e., when there is a non-linear relationship between the parameters and the dynamical model, both DA methods give inexact results. Moreover, several studies have revealed that for non-linear cases the EnKF and ES give different approximation errors. We recently conducted a thorough investigation of sequential and non-sequential assimilation schemes. The investigation showed that, for a series of weakly non-linear data, sequential assimilation is favorable to non-sequential assimilation. In addition, analytical, and numerical, evidence showed that by ordering data after ascending non-linearity, one reduces the approximation error for the sequential scheme. Ordering of data will, however, not reduce the approximation error for all cases. It is clear that for a sequence of highly non-linear data the approximate methods, independent of how the data are ordered, will fail. Likewise, if the data has little variation in non-linearity, nothing is gain by ordered sequential assimilation. In this work, we investigate, by simple toy models, for which range of data non-linearity there is a potential advantage of ordered sequential assimilation. Furthermore, considering a 2D reservoir case, we evaluate the non-linearity for a collection of production data and production strategies. For each numerical setup, we assess the benefit from ordered sequential assimilation of the data, and we compare the results with results obtained by the toy models. The assimilation schemes are assessed by comparing their history matching capabilities, and by measuring the stochastic distances between their posterior distributions and the posterior distribution obtained by a Markov chain Monte Carlo algorithm. Throughout, the non-linearity is evaluated by a stochastic non-linearity measure.